Accurate flexible fitting of high-resolution protein structures into cryo-electron microscopy maps using coarse-grained pseudo-energy minimization

MDFF_NM: Improved Molecular Dynamics Flexible Fitting into Cryo-EM Density Maps with a Multireplica Normal Mode-Based Search

Molecular Dynamics Flexible Fitting (MDFF) is a widely used tool to refine high-resolution structures into cryo-EM density maps. Despite many successful applications, MDFF is still limited by its high computational cost, overfitting, accuracy, and performance issues due to entrapment within wrong local minima. Modern ensemble-based MDFF tools have generated promising results in the past decade. In line with these studies, we present MDFF_NM, a stochastic hybrid flexible fitting algorithm combining Normal Mode Analysis (NMA) and simulation-based flexible fitting. Initial tests reveal that, besides accelerating the fitting process, MDFF_NM increases the diversity of fitting routes leading to the target, uncovering ensembles of conformations in closer agreement with experimental data. The potential integration of MDFF_NM with other existing methods and integrative modeling pipelines is also discussed.

Modeling and Simulation of the NMDA Receptor at Coarse-Grained and Atomistic Levels

N-Methyl-D-aspartate (NMDA) receptors are glutamate-gated excitatory channels that play essential roles in brain functions. While high-resolution structures were solved for an allosterically inhibited form of functional NMDA receptor, other key functional states (particularly the active open-channel state) have not yet been resolved at atomic resolutions. To decrypt the molecular mechanism of the NMDA receptor activation, structural modeling and simulation are instrumental in providing detailed information about the dynamics and energetics of the receptor in various functional states. In this chapter, we describe coarse-grained modeling of the NMDA receptor using an elastic network model and related modeling/analysis tools (e.g., normal mode analysis, flexibility and hotspot analysis, cryo-EM flexible fitting, and transition pathway modeling) based on available structures. Additionally, we show how to build an atomistic model of the active-state receptor with targeted molecular dynamics (MD) simulation and explore its energetics and dynamics with conventional MD simulation. Taken together, these modeling and simulation can offer rich structural and dynamic information which will guide experimental studies of the activation of this key receptor.

Explicit versus implicit consideration of binding partners in protein-protein complex to elucidate intrinsic dynamics

The binding of many proteins to their protein partners is tightly regulated via control of their relative intrinsic dynamics during the binding process, a phenomenon which can in turn be modulated. Therefore, investigating the intrinsic dynamics of proteins is necessary to understand function in a comprehensive way. By intrinsic dynamics herein, we principally refer to the vibrational signature of a protein molecule popularly obtained from normal modes or essential modes. For normal modes, one often considers that the molecule under investigation is a collection of springs in a solvent-free or implicit-solvent medium. In the context of a protein-binding partner, the analysis of vibration of the target protein is often complicated due to molecular interaction within the complex. Generally, it is assumed that the isolated bound conformation of the target protein captures the implicit effect of the binding partner on the intrinsic dynamics, therefore suggesting that any influence of the partner molecule is also already integrated. Such an assumption allows large-scale studies of the conservation of protein flexibility. However, in cases where a partner protein directly influences the vibration of the target via critical contacts at the protein-protein interface, the above assumption falls short of providing a detailed view. In this review article, we discuss the implications of considering the dynamics of a protein in a protein-protein complex, as modelled implicitly and explicitly with methods dependent on elastic network models. We further propose how such an explicit consideration can be applied to understand critical protein-protein contacts that can be targeted in future studies.

Simulation and Machine Learning Methods for Ion-Channel Structure Determination, Mechanistic Studies and Drug Design

Ion channels are expressed in almost all living cells, controlling the in-and-out communications, making them ideal drug targets, especially for central nervous system diseases. However, owing to their dynamic nature and the presence of a membrane environment, ion channels remain difficult targets for the past decades. Recent advancement in cryo-electron microscopy and computational methods has shed light on this issue. An explosion in high-resolution ion channel structures paved way for structure-based rational drug design and the state-of-the-art simulation and machine learning techniques dramatically improved the efficiency and effectiveness of computer-aided drug design. Here we present an overview of how simulation and machine learning-based methods fundamentally changed the ion channel-related drug design at different levels, as well as the emerging trends in the field.

Exploring cryo-electron microscopy with molecular dynamics

Single particle analysis cryo-electron microscopy (EM) and molecular dynamics (MD) have been complimentary methods since cryo-EM was first applied to the field of structural biology. The relationship started by biasing structural models to fit low-resolution cryo-EM maps of large macromolecular complexes not amenable to crystallization. The connection between cryo-EM and MD evolved as cryo-EM maps improved in resolution, allowing advanced sampling algorithms to simultaneously refine backbone and sidechains. Moving beyond a single static snapshot, modern inferencing approaches integrate cryo-EM and MD to generate structural ensembles from cryo-EM map data or directly from the particle images themselves. We summarize the recent history of MD innovations in the area of cryo-EM modeling. The merits for the myriad of MD based cryo-EM modeling methods are discussed, as well as, the discoveries that were made possible by the integration of molecular modeling with cryo-EM. Lastly, current challenges and potential opportunities are reviewed.

HOPMA: Boosting Protein Functional Dynamics with Colored Contact Maps

In light of the recent very rapid progress in protein structure prediction, accessing the multitude of functional protein states is becoming more central than ever before. Indeed, proteins are flexible macromolecules, and they often perform their function by switching between different conformations. However, high-resolution experimental techniques such as X-ray crystallography and cryogenic electron microscopy can catch relatively few protein functional states. Many others are only accessible under physiological conditions in solution. Therefore, there is a pressing need to fill this gap with computational approaches. We present HOPMA, a novel method to predict protein functional states and transitions by using a modified elastic network model. The method exploits patterns in a protein contact map, taking its 3D structure as input, and excludes some disconnected patches from the elastic network. Combined with nonlinear normal mode analysis, this strategy boosts the protein conformational space exploration, especially when the input structure is highly constrained, as we demonstrate on a set of more than 400 transitions. Our results let us envision the discovery of new functional conformations, which were unreachable previously, starting from the experimentally known protein structures. The method is computationally efficient and available at https://github.com/elolaine/HOPMA and https://team.inria.fr/nano-d/software/nolb-normal-modes.

Computational Ways to Enhance Protein Inhibitor Design

Two new computational approaches are described to aid in the design of new peptide-based drugs by evaluating ensembles of protein structures from their dynamics and through the assessing of structures using empirical contact potential. These approaches build on the concept that conformational variability can aid in the binding process and, for disordered proteins, can even facilitate the binding of more diverse ligands. This latter consideration indicates that such a design process should be less restrictive so that multiple inhibitors might be effective. The example chosen here focuses on proteins/peptides that bind to hemagglutinin (HA) to block the large-scale conformational change for activation. Variability in the conformations is considered from sets of experimental structures, or as an alternative, from their simple computed dynamics; the set of designe peptides/small proteins from the David Baker lab designed to bind to hemagglutinin, is the large set considered and is assessed with the new empirical contact potentials.

Hybrid methods for combined experimental and computational determination of protein structure

Knowledge of protein structure is paramount to the understanding of biological function, developing new therapeutics, and making detailed mechanistic hypotheses. Therefore, methods to accurately elucidate three-dimensional structures of proteins are in high demand. While there are a few experimental techniques that can routinely provide high-resolution structures, such as x-ray crystallography, nuclear magnetic resonance (NMR), and cryo-EM, which have been developed to determine the structures of proteins, these techniques each have shortcomings and thus cannot be used in all cases. However, additionally, a large number of experimental techniques that provide some structural information, but not enough to assign atomic positions with high certainty have been developed. These methods offer sparse experimental data, which can also be noisy and inaccurate in some instances. In cases where it is not possible to determine the structure of a protein experimentally, computational structure prediction methods can be used as an alternative. Although computational methods can be performed without any experimental data in a large number of studies, inclusion of sparse experimental data into these prediction methods has yielded significant improvement. In this Perspective, we cover many of the successes of integrative modeling, computational modeling with experimental data, specifically for protein folding, protein-protein docking, and molecular dynamics simulations. We describe methods that incorporate sparse data from cryo-EM, NMR, mass spectrometry, electron paramagnetic resonance, small-angle x-ray scattering, Förster resonance energy transfer, and genetic sequence covariation. Finally, we highlight some of the major challenges in the field as well as possible future directions.

Predicting Protein Functional Motions: an Old Recipe with a New Twist

Large macromolecules, including proteins and their complexes, very often adopt multiple conformations. Some of them can be seen experimentally, for example with x-ray crystallography or cryo-electron microscopy. This structural heterogeneity is not occasional and is frequently linked with specific biological function. Thus, the accurate description of macromolecular conformational transitions is crucial for understanding fundamental mechanisms of life's machinery. We report on a real-time method to predict such transitions by extrapolating from instantaneous eigen motions, computed using the normal mode analysis, to a series of twists. We demonstrate the applicability of our approach to the prediction of a wide range of motions, including large collective opening-closing transitions and conformational changes induced by partner binding. We also highlight particularly difficult cases of very small transitions between crystal and solution structures. Our method guarantees preservation of the protein structure during the transition and allows accessing conformations that are unreachable with classical normal mode analysis. We provide practical solutions to describe localized motions with a few low-frequency modes and to relax some geometrical constraints along the predicted transitions. This work opens the way to the systematic description of protein motions, whatever their degree of collectivity. Our method is freely available as a part of the NOn-Linear rigid Block (NOLB) package.

Advances in Structure Modeling Methods for Cryo-Electron Microscopy Maps

Cryo-electron microscopy (cryo-EM) has now become a widely used technique for structure determination of macromolecular complexes. For modeling molecular structures from density maps of different resolutions, many algorithms have been developed. These algorithms can be categorized into rigid fitting, flexible fitting, and de novo modeling methods. It is also observed that machine learning (ML) techniques have been increasingly applied following the rapid progress of the ML field. Here, we review these different categories of macromolecule structure modeling methods and discuss their advances over time.

Modelling structures in cryo-EM maps

Recent advances in structure determination of sub-cellular structures using cryo-electron microscopy and tomography have enabled us to understand their architecture in a more detailed manner and gain insight into their function. The choice of approach to use for atomic model building, fitting, refinement and validation in the 3D map resulting from these experiments depends primarily on the resolution of the map and the prior information on the corresponding model. Here, we survey some of such methods and approaches and highlight their uses in specific recent examples.

Cryo_fit: Democratization of flexible fitting for cryo-EM

Cryo-electron microscopy (cryo-EM) is becoming a method of choice for describing native conformations of biomolecular complexes at high resolution. The rapid growth of cryo-EM in recent years has created a high demand for automated solutions, both in hardware and software. Flexible fitting of atomic models to three-dimensional (3D) cryo-EM reconstructions by molecular dynamics (MD) simulation is a popular technique but often requires technical expertise in computer simulation. This work introduces cryo_fit, a package for the automatic flexible fitting of atomic models in cryo-EM maps using MD simulation. The package is integrated with the Phenix software suite. The module was designed to automate the multiple steps of MD simulation in a reproducible manner, as well as facilitate refinement and validation through Phenix. Through the use of cryo_fit, scientists with little experience in MD simulation can produce high quality atomic models automatically and better exploit the potential of cryo-EM.

Normal Mode Analysis as a Routine Part of a Structural Investigation

Normal mode analysis (NMA) is a technique that can be used to describe the flexible states accessible to a protein about an equilibrium position. These states have been shown repeatedly to have functional significance. NMA is probably the least computationally expensive method for studying the dynamics of macromolecules, and advances in computer technology and algorithms for calculating normal modes over the last 20 years have made it nearly trivial for all but the largest systems. Despite this, it is still uncommon for NMA to be used as a component of the analysis of a structural study. In this review, we will describe NMA, outline its advantages and limitations, explain what can and cannot be learned from it, and address some criticisms and concerns that have been voiced about it. We will then review the most commonly used techniques for reducing the computational cost of this method and identify the web services making use of these methods. We will illustrate several of their possible uses with recent examples from the literature. We conclude by recommending that NMA become one of the standard tools employed in any structural study.

Protein secondary structure detection in intermediate-resolution cryo-EM maps using deep learning

An increasing number of protein structures have been solved by cryo-electron microscopy (cryo-EM). Although structures determined at near-atomic resolution are now routinely reported, many density maps are still determined at an intermediate resolution, where extracting structure information is still a challenge. We have developed a computational method, Emap2sec, which identifies the secondary structures of proteins (α helices, β sheets, and other structures) in an EM map of 5 to 10 Å resolution. Emap2sec uses a 3D deep convolutional neural network to assign secondary structure to each grid point in an EM map. We tested Emap2sec on 6.0 and 10.0 Å resolution EM maps simulated from 34 structures, as well as on 43 maps determined experimentally at 5.0 to 9.5 Å resolution. Emap2sec was able to clearly identify the secondary structures in many maps tested, and showed substantially better performance than existing methods.

Simultaneous Determination of Protein Structure and Dynamics Using Cryo-Electron Microscopy

Cryo-electron microscopy is rapidly emerging as a powerful technique to determine the structures of complex macromolecular systems elusive to other techniques. Because many of these systems are highly dynamical, characterizing their movements is also a crucial step to unravel their biological functions. To achieve this goal, we report an integrative modeling approach to simultaneously determine structure and dynamics of macromolecular systems from cryo-electron microscopy density maps. By quantifying the level of noise in the data and dealing with their ensemble-averaged nature, this approach enables the integration of multiple sources of information to model ensembles of structures and infer their populations. We illustrate the method by characterizing structure and dynamics of the integral membrane receptor STRA6, thus providing insights into the mechanisms by which it interacts with retinol binding protein and translocates retinol across the membrane.

Bayesian Weighing of Electron Cryo-Microscopy Data for Integrative Structural Modeling

Cryo-electron microscopy (cryo-EM) has become a mainstream technique for determining the structures of complex biological systems. However, accurate integrative structural modeling has been hampered by the challenges in objectively weighing cryo-EM data against other sources of information due to the presence of random and systematic errors, as well as correlations, in the data. To address these challenges, we introduce a Bayesian scoring function that efficiently and accurately ranks alternative structural models of a macromolecular system based on their consistency with a cryo-EM density map as well as other experimental and prior information. The accuracy of this approach is benchmarked using complexes of known structure and illustrated in three applications: the structural determination of the GroEL/GroES, RNA polymerase II, and exosome complexes. The approach is implemented in the open-source Integrative Modeling Platform (http://integrativemodeling.org), thus enabling integrative structure determination by combining cryo-EM data with other sources of information.

Accurate flexible refinement of atomic models against medium-resolution cryo-EM maps using damped dynamics

BACKGROUND

Dramatic progress has recently been made in cryo-electron microscopy technologies, which now make possible the reconstruction of a growing number of biomolecular structures to near-atomic resolution. However, the need persists for fitting and refinement approaches that address those cases that require modeling assistance.

METHODS

In this paper, we describe algorithms to optimize the performance of such medium-resolution refinement methods. These algorithms aim to automatically optimize the parameters that define the density shape of the flexibly fitted model, as well as the time-dependent damper cutoff distance. Atomic distance constraints can be prescribed for cases where extra containment of parts of the structure is helpful, such as in regions where the density map is poorly defined. Also, we propose a simple stopping criterion that estimates the probable onset of overfitting during the simulation.

RESULTS

The new set of algorithms produce more accurate fitting and refinement results, and yield a faster rate of convergence of the trajectory toward the fitted conformation. The latter is also more reliable due to the overfitting warning provided to the user.

CONCLUSIONS

The algorithms described here were implemented in the new Damped-Dynamics Flexible Fitting simulation tool "DDforge" in the Situs package.

Investigating the structural dynamics of the PIEZO1 channel activation and inactivation by coarse-grained modeling

The PIEZO channels, a family of mechanosensitive channels in vertebrates, feature a fast activation by mechanical stimuli (eg, membrane tension) followed by a slower inactivation. Although a medium-resolution structure of the trimeric form of PIEZO1 was solved by cryo-electron microscopy (cryo-EM), key structural changes responsible for the channel activation and inactivation are still unknown. Toward decrypting the structural mechanism of the PIEZO1 activation and inactivation, we performed systematic coarse-grained modeling using an elastic network model and related modeling/analysis tools (ie, normal mode analysis, flexibility and hotspot analysis, correlation analysis, and cryo-EM-based hybrid modeling and flexible fitting). We identified four key motional modes that may drive the tension-induced activation and inactivation, with fast and slow relaxation time, respectively. These modes allosterically couple the lateral and vertical motions of the peripheral domains to the opening and closing of the intra-cellular vestibule, enabling external mechanical forces to trigger, and regulate the activation/inactivation transitions. We also calculated domain-specific flexibility profiles, and predicted hotspot residues at key domain-domain interfaces and hinges. Our results offer unprecedented structural and dynamic information, which is consistent with the literature on mutational and functional studies of the PIEZO channels, and will guide future studies of this important family of mechanosensitive channels.

Probing the Structural Dynamics of the NMDA Receptor Activation by Coarse-Grained Modeling

N-Methyl-D-aspartate (NMDA) receptors are glutamate-gated excitatory channels that play essential roles in brain functions. High-resolution structures have been solved for an allosterically inhibited and agonist-bound form of a functional NMDA receptor; however, other key functional states (particularly the active open-channel state) were only resolved at moderate resolutions by cryo-electron microscopy (cryo-EM). To decrypt the mechanism of the NMDA receptor activation, structural modeling is essential to provide presently missing information about structural dynamics. We performed systematic coarse-grained modeling using an elastic network model and related modeling/analysis tools (e.g., normal mode analysis, flexibility and hotspot analysis, cryo-EM flexible fitting, and transition pathway modeling) based on an active-state cryo-EM map. We observed extensive conformational changes that allosterically couple the extracellular regulatory and agonist-binding domains to the pore-forming trans-membrane domain (TMD), and validated these, to our knowledge, new observations against known mutational and functional studies. Our results predict two key modes of collective motions featuring shearing/twisting of the extracellular domains relative to the TMD, reveal subunit-specific flexibility profiles, and identify functional hotspot residues at key domain-domain interfaces. Finally, by examining the conformational transition pathway between the allosterically inhibited form and the active form, we predict a discrete sequence of domain motions, which propagate from the extracellular domains to the TMD. In summary, our results offer rich structural and dynamic information, which is consistent with the literature on structure-function relationships in NMDA receptors, and will guide in-depth studies on the activation dynamics of this important neurotransmitter receptor.

Flexible Fitting of Atomic Models into Cryo-EM Density Maps Guided by Helix Correspondences

Although electron cryo-microscopy (cryo-EM) has recently achieved resolutions of better than 3 Å, at which point molecular modeling can be done directly from the density map, analysis and annotation of a cryo-EM density map still primarily rely on fitting atomic or homology models to the density map. In this article, we present, to our knowledge, a new method for flexible fitting of known or modeled protein structures into cryo-EM density maps. Unlike existing methods that are guided by local density gradients, our method is guided by correspondences between the α-helices in the density map and model, and does not require an initial rigid-body fitting step. Compared with current methods on both simulated and experimental density maps, our method not only achieves greater accuracy for proteins with large deformations but also runs as fast or faster than many of the other flexible fitting routines.

Unraveling low-resolution structural data of large biomolecules by constructing atomic models with experiment-targeted parallel cascade selection simulations

Various low-resolution experimental techniques have gained more and more popularity in obtaining structural information of large biomolecules. In order to interpret the low-resolution structural data properly, one may need to construct an atomic model of the biomolecule by fitting the data using computer simulations. Here we develop, to our knowledge, a new computational tool for such integrative modeling by taking the advantage of an efficient sampling technique called parallel cascade selection (PaCS) simulation. For given low-resolution structural data, this PaCS-Fit method converts it into a scoring function. After an initial simulation starting from a known structure of the biomolecule, the scoring function is used to pick conformations for next cycle of multiple independent simulations. By this iterative screening-after-sampling strategy, the biomolecule may be driven towards a conformation that fits well with the low-resolution data. Our method has been validated using three proteins with small-angle X-ray scattering data and two proteins with electron microscopy data. In all benchmark tests, high-quality atomic models, with generally 1-3 Å from the target structures, are obtained. Since our tool does not need to add any biasing potential in the simulations to deform the structure, any type of low-resolution data can be implemented conveniently.

Probing the folded state and mechanical unfolding pathways of T4 lysozyme using all-atom and coarse-grained molecular simulation

The Bacteriophage T4 Lysozyme (T4L) is a prototype modular protein comprised of an N-terminal and a C-domain domain, which was extensively studied to understand the folding/unfolding mechanism of modular proteins. To offer detailed structural and dynamic insights to the folded-state stability and the mechanical unfolding behaviors of T4L, we have performed extensive equilibrium and steered molecular dynamics simulations of both the wild-type (WT) and a circular permutation (CP) variant of T4L using all-atom and coarse-grained force fields. Our all-atom and coarse-grained simulations of the folded state have consistently found greater stability of the C-domain than the N-domain in isolation, which is in agreement with past thermostatic studies of T4L. While the all-atom simulation cannot fully explain the mechanical unfolding behaviors of the WT and the CP variant observed in an optical tweezers study, the coarse-grained simulations based on the Go model or a modified elastic network model (mENM) are in qualitative agreement with the experimental finding of greater unfolding cooperativity in the WT than the CP variant. Interestingly, the two coarse-grained models predict different structural mechanisms for the observed change in cooperativity between the WT and the CP variant--while the Go model predicts minor modification of the unfolding pathways by circular permutation (i.e., preserving the general order that the N-domain unfolds before the C-domain), the mENM predicts a dramatic change in unfolding pathways (e.g., different order of N/C-domain unfolding in the WT and the CP variant). Based on our simulations, we have analyzed the limitations of and the key differences between these models and offered testable predictions for future experiments to resolve the structural mechanism for cooperative folding/unfolding of T4L.

Decrypting the structural, dynamic, and energetic basis of a monomeric kinesin interacting with a tubulin dimer in three ATPase states by all-atom molecular dynamics simulation

We have employed molecular dynamics (MD) simulation to investigate, with atomic details, the structural dynamics and energetics of three major ATPase states (ADP, APO, and ATP state) of a human kinesin-1 monomer in complex with a tubulin dimer. Starting from a recently solved crystal structure of ATP-like kinesin-tubulin complex by the Knossow lab, we have used flexible fitting of cryo-electron-microscopy maps to construct new structural models of the kinesin-tubulin complex in APO and ATP state, and then conducted extensive MD simulations (total 400 ns for each state), followed by flexibility analysis, principal component analysis, hydrogen bond analysis, and binding free energy analysis. Our modeling and simulation have revealed key nucleotide-dependent changes in the structure and flexibility of the nucleotide-binding pocket (featuring a highly flexible and open switch I in APO state) and the tubulin-binding site, and allosterically coupled motions driving the APO to ATP transition. In addition, our binding free energy analysis has identified a set of key residues involved in kinesin-tubulin binding. On the basis of our simulation, we have attempted to address several outstanding issues in kinesin study, including the possible roles of β-sheet twist and neck linker docking in regulating nucleotide release and binding, the structural mechanism of ADP release, and possible extension and shortening of α4 helix during the ATPase cycle. This study has provided a comprehensive structural and dynamic picture of kinesin's major ATPase states, and offered promising targets for future mutational and functional studies to investigate the molecular mechanism of kinesin motors.

Zooming in on disordered systems: neutron reflection studies of proteins associated with fluid membranes

Neutron reflectometry (NR) is an emerging experimental technique for the structural characterization of proteins interacting with fluid bilayer membranes under conditions that mimic closely the cellular environment. Thus, cellular processes can be emulated in artificial systems and their molecular basis studied by adding cellular components one at a time in a well-controlled environment while the resulting structures, or structural changes in response to external cues, are monitored with neutron reflection. In recent years, sample environments, data collection strategies and data analysis were continuously refined. The combination of these improvements increases the information which can be obtained from NR to an extent that enables structural characterization of protein-membrane complexes at a length scale that exceeds the resolution of the measurement by far. Ultimately, the combination of NR with molecular dynamics (MD) simulations can be used to cross-validate the results of the two techniques and provide atomic-scale structural models. This review discusses these developments in detail and demonstrates how they provide new windows into relevant biomedical problems. This article is part of a Special Issue entitled: Interfacially Active Peptides and Proteins. Guest Editors: William C. Wimley and Kalina Hristova.

High-resolution modeling of protein structures based on flexible fitting of low-resolution structural data

To circumvent the difficulty of directly solving high-resolution biomolecular structures, low-resolution structural data from Cryo-electron microscopy (EM) and small angle solution X-ray scattering (SAXS) are increasingly used to explore multiple conformational states of biomolecular assemblies. One promising venue to obtain high-resolution structural models from low-resolution data is via data-constrained flexible fitting. To this end, we have developed a new method based on a coarse-grained Cα-only protein representation, and a modified form of the elastic network model (ENM) that allows large-scale conformational changes while maintaining the integrity of local structures including pseudo-bonds and secondary structures. Our method minimizes a pseudo-energy which linearly combines various terms of the modified ENM energy with an EM/SAXS-fitting score and a collision energy that penalizes steric collisions. Unlike some previous flexible fitting efforts using the lowest few normal modes, our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled with accuracy. This method is also highly efficient in computing time. We have demonstrated our method using adenylate kinase as a test case which undergoes a large open-to-close conformational change. The EM-fitting method is available at a web server (http://enm.lobos.nih.gov), and the SAXS-fitting method is available as a pre-compiled executable upon request.

The joys and perils of flexible fitting

While performing their functions, biological macromolecules often form large, dynamically changing macromolecular assemblies. Only a relatively small number of such assemblies have been accessible to the atomic-resolution techniques X-ray crystallography and NMR. Electron microscopy in conjunction with image reconstruction has become the preferred alternative for revealing the structures of such macromolecular complexes. However, for most assemblies the achievable resolution is too low to allow accurate atomic modeling directly from the data. Yet, useful models often can be obtained by fitting atomic models of individual components into a low-resolution reconstruction of the entire assembly. Several algorithms for achieving optimal fits in this context were developed recently, many allowing considerable degrees of flexibility to account for binding-induced conformational changes of the assembly components. This chapter describes the advantages and potential pitfalls of these methods and puts them into perspective with alternative approaches such as iterative modular fitting of rigid-body domains.

iMODFIT: efficient and robust flexible fitting based on vibrational analysis in internal coordinates

Here, we employed the collective motions extracted from Normal Mode Analysis (NMA) in internal coordinates (torsional space) for the flexible fitting of atomic-resolution structures into electron microscopy (EM) density maps. The proposed methodology was validated using a benchmark of simulated cases, highlighting its robustness over the full range of EM resolutions and even over coarse-grained representations. A systematic comparison with other methods further showcased the advantages of this proposed methodology, especially at medium to lower resolutions. Using this method, computational costs and potential overfitting problems are naturally reduced by constraining the search in low-frequency NMA space, where covalent geometry is implicitly maintained. This method also effectively captures the macromolecular changes of a representative set of experimental test cases. We believe that this novel approach will extend the currently available EM hybrid methods to the atomic-level interpretation of large conformational changes and their functional implications.

Targeted conformational search with map-restrained self-guided Langevin dynamics: application to flexible fitting into electron microscopic density maps

We present a map-restrained self-guided Langevin dynamics (MapSGLD) simulation method for efficient targeted conformational search. The targeted conformational search represents simulations under restraints defined by experimental observations and/or by user specified structural requirements. Through map-restraints, this method provides an efficient way to maintain substructures and to set structure targets during conformational searching. With an enhanced conformational searching ability of self-guided Langevin dynamics, this approach is suitable for simulating large-scale conformational changes, such as the formation of macromolecular assemblies and transitions between different conformational states. Using several examples, we illustrate the application of this method in flexible fitting of atomic structures into density maps derived from cryo-electron microscopy.

NONUNIFORM FOURIER TRANSFORMS FOR RIGID-BODY AND MULTI-DIMENSIONAL ROTATIONAL CORRELATIONS

The task of evaluating correlations is central to computational structural biology. The rigid-body correlation problem seeks the rigid-body transformation (R, t), R ∈ SO(3), t ∈ ℝ³ that maximizes the correlation between a pair of input scalar-valued functions representing molecular structures. Exhaustive solutions to the rigid-body correlation problem take advantage of the fast Fourier transform to achieve a speedup either with respect to the sought translation or rotation. We present PFcorr, a new exhaustive solution, based on the non-equispaced SO(3) Fourier transform, to the rigid-body correlation problem; unlike previous solutions, ours achieves a combination of translational and rotational speedups without requiring equispaced grids. PFcorr can be straightforwardly applied to a variety of problems in protein structure prediction and refinement that involve correlations under rigid-body motions of the protein. Additionally, we show how it applies, along with an appropriate flexibility model, to analogs of the above problems in which the flexibility of the protein is relevant.

Computational methods for constructing protein structure models from 3D electron microscopy maps

Protein structure determination by cryo-electron microscopy (EM) has made significant progress in the past decades. Resolutions of EM maps have been improving as evidenced by recently reported structures that are solved at high resolutions close to 3Å. Computational methods play a key role in interpreting EM data. Among many computational procedures applied to an EM map to obtain protein structure information, in this article we focus on reviewing computational methods that model protein three-dimensional (3D) structures from a 3D EM density map that is constructed from two-dimensional (2D) maps. The computational methods we discuss range from de novo methods, which identify structural elements in an EM map, to structure fitting methods, where known high resolution structures are fit into a low-resolution EM map. A list of available computational tools is also provided.

Consensus among multiple approaches as a reliability measure for flexible fitting into cryo-EM data

Cryo-electron microscopy (cryo-EM) can provide low-resolution density maps of large macromolecular assemblies. As the number of structures deposited in the Protein Data Bank by fitting a high-resolution structure into a low-resolution cryo-EM map is increasing, there is a need to revise the protocols and improve the measures for fitting. A recent study suggested using a combination of multiple automated flexible fitting approaches to improve the interpretation of cryo-EM data. The current work further explores the use of multiple approaches by validating this "consensus" fitting approach and deriving a local reliability measure. Here four different flexible fitting approaches are applied for fitting an initial structure into a simulated density map of known target structure from a dataset of proteins. It is found that the models produced from different approaches often have a consensus in conformation and are also near to the target structure, whereas cases not showing consensus are away from the target. A high correlation is also observed between the RMSF profiles calculated with respect to the average and the target structures, which indicates that the relation between consensus and accuracy can also be extended to a per-residue level. Therefore, the RMSF among the fitted models is proposed as a local reliability measure, which can be used to assess the reliability of the fit at specific regions. Hence, we encourage the community to use consensus flexible fitting with different methods to report on local reliability of the resulting models and improve the interpretation of cryo-EM data.

Structure-based simulations of the translocation mechanism of the hepatitis C virus NS3 helicase along single-stranded nucleic acid

The NS3 helicase of Hepatitis C virus is an ATP-fueled molecular motor that can translocate along single-stranded (ss) nucleic acid, and unwind double-stranded nucleic acids. It makes a promising antiviral target and an important prototype system for helicase research. Despite recent progress, the detailed mechanism of NS3 helicase remains unknown. In this study, we have combined coarse-grained (CG) and atomistic simulations to probe the translocation mechanism of NS3 helicase along ssDNA. At the residue level of detail, our CG simulations have captured functionally important interdomain motions of NS3 helicase and reproduced single-base translocation of NS3 helicase along ssDNA in the 3'-5' direction, which is in good agreement with experimental data and the inchworm model. By combining the CG simulations with residue-specific perturbations to protein-DNA interactions, we have identified a number of key residues important to the translocation machinery that agree with previous structural and mutational studies. Additionally, our atomistic simulations with targeted molecular dynamics have corroborated the findings of CG simulations and further revealed key protein-DNA hydrogen bonds that break/form during the transitions. This study offers, to our knowledge, the most detailed and realistic simulations of translocation mechanism of NS3 helicase. The simulation protocol established in this study will be useful for designing inhibitors that target the translocation machinery of NS3 helicase, and for simulations of a variety of nucleic-acid-based molecular motors.

Coarse-grained and all-atom modeling of structural states and transitions in hemoglobin

Hemoglobin (Hb), an oxygen-binding protein composed of four subunits (α1, α2, β1, and β2), is a well-known example of allosteric proteins that are capable of cooperative ligand binding. Despite decades of studies, the structural basis of its cooperativity remains controversial. In this study, we have integrated coarse-grained (CG) modeling, all-atom simulation, and structural data from X-ray crystallography and wide-angle X-ray scattering (WAXS), aiming to probe dynamic properties of the two structural states of Hb (T and R state) and the transitions between them. First, by analyzing the WAXS data of unliganded and liganded Hb, we have found that the structural ensemble of T or R state is dominated by one crystal structure of Hb with small contributions from other crystal structures of Hb. Second, we have used normal mode analysis to identify two distinct quaternary rotations between the α1β1 and α2β2 dimer, which drive the transitions between T and R state. We have also identified the hot-spot residues whose mutations are predicted to greatly change these quaternary motions. Third, we have generated a CG transition pathway between T and R state, which predicts a clear order of quaternary and tertiary changes involving α and β subunits in Hb. Fourth, we have used the accelerated molecular dynamics to perform an all-atom simulation starting from the T state of Hb, and we have observed a transition toward the R state of Hb. Further analysis of crystal structural data and the all-atom simulation trajectory has corroborated the order of quaternary and tertiary changes predicted by CG modeling.

Real-space refinement with DireX: from global fitting to side-chain improvements

Single-particle cryo-electron microscopy (cryo-EM) has become an important tool to determine the structure of large biomolecules and assemblies thereof. However, the achievable resolution varies considerably over a wide range of about 3.5-20 Å. The interpretation of these intermediate- to low-resolution density maps in terms of atomic models is a big challenge and an area of active research. Here, we present our real-space structure refinement program DireX, which was developed primarily for cryo-EM-derived density maps. The basic principle and its main features are described. DireX employs Deformable Elastic Network (DEN) restraints to reduce overfitting by decreasing the effective number of degrees of freedom used in the refinement. Missing or reduced density due to flexible parts of the protein can lead to artifacts in the structure refinement, which is addressed through the concept of restrained grouped occupancy refinement. Furthermore, we describe the performance of DireX in the 2010 Cryo-EM Modeling Challenge, where we chose six density maps of four different proteins provided by the Modeling Challenge exemplifying typical refinement results at a large resolution range from 3 to 23 Å.

Macromolecular structure modeling from 3D EM using VolRover 2.0

We review tools for structure identification and model-based refinement from three-dimensional electron microscopy implemented in our in-house software package, VOLROVER 2.0. For viral density maps with icosahedral symmetry, we segment the capsid, polymeric, and monomeric subunits using techniques based on automatic symmetry detection and multidomain fast marching. For large biomolecules without symmetry information, we again use our multidomain fast-marching method with manual or fit-based multiseeding to segment meaningful substructures. In either case, we subject the resulting segmented subunit to secondary structure detection when the EM resolution is sufficiently high, and rigid-body structure fitting when the corresponding X-ray structure is available. Secondary structure elements are identified by three techniques: our earlier volume-based and boundary-based skeletonization methods as well as a new method, currently in development, based on solving the grassfire flow equation. For rigid-body fitting, we adapt our earlier fast Fourier-based correlation scheme F2Dock. Our reported segmentation, secondary structure elements identification, and rigid-body fitting techniques, implemented in VOLROVER 2.0 are applied to the PSB 2011 cryo-EM modeling challenge data, and our results are briefly compared to similar results submitted from other research groups. The comparisons show that our techniques are equally capable of segmenting relatively accurate subunits from a viral or protein assembly, and that high segmentation quality leads in turn to higher-quality results of secondary structure elements identification and correlation-based rigid-body fitting. © 2012 Wiley Periodicals, Inc. Biopolymers 97: 709-731, 2012.

Go hybrid: EM, crystallography, and beyond

A mechanistic understanding of the molecular transactions that govern cellular function requires knowledge of the dynamic organization of the macromolecular machines involved in these processes. Structural biologists employ a variety of biophysical methods to study large macromolecular complexes, but no single technique is likely to provide a complete description of the structure-function relationship of all the constituent components. Since structural studies generally only provide snapshots of these dynamic machines as they accomplish their molecular functions, combining data from many methodologies is crucial to our understanding of molecular function.

All-atom structural investigation of kinesin-microtubule complex constrained by high-quality cryo-electron-microscopy maps

In this study, we have performed a comprehensive structural investigation of three major biochemical states of a kinesin complexed with microtubule under the constraint of high-quality cryo-electron-microscopy (EM) maps. In addition to the ADP and ATP state which were captured by X-ray crystallography, we have also modeled the nucleotide-free or APO state for which no crystal structure is available. We have combined flexible fitting of EM maps with regular molecular dynamics simulations, hydrogen-bond analysis, and free energy calculation. Our APO-state models feature a subdomain rotation involving loop L2 and α6 helix of kinesin, and local structural changes in active site similar to a related motor protein, myosin. We have identified a list of hydrogen bonds involving key residues in the active site and the binding interface between kinesin and microtubule. Some of these hydrogen bonds may play an important role in coupling microtubule binding to ATPase activities in kinesin. We have validated our models by calculating the binding free energy between kinesin and microtubule, which quantitatively accounts for the observation of strong binding in the APO and ATP state and weak binding in the ADP state. This study will offer promising targets for future mutational and functional studies to investigate the mechanism of kinesin motors.

Fitting multimeric protein complexes into electron microscopy maps using 3D Zernike descriptors

A novel computational method for fitting high-resolution structures of multiple proteins into a cryoelectron microscopy map is presented. The method named EMLZerD generates a pool of candidate multiple protein docking conformations of component proteins, which are later compared with a provided electron microscopy (EM) density map to select the ones that fit well into the EM map. The comparison of docking conformations and the EM map is performed using the 3D Zernike descriptor (3DZD), a mathematical series expansion of three-dimensional functions. The 3DZD provides a unified representation of the surface shape of multimeric protein complex models and EM maps, which allows a convenient, fast quantitative comparison of the three-dimensional structural data. Out of 19 multimeric complexes tested, near native complex structures with a root-mean-square deviation of less than 2.5 Å were obtained for 14 cases while medium range resolution structures with correct topology were computed for the additional 5 cases.

Elastic Network Models are Robust to Variations in Formalism

Understanding the functions of biomolecules requires insight not only from structures, but from dynamics as well. Often, the most interesting processes occur on time scales too slow for exploration by conventional molecular dynamics (MD) simulations. For this reason, alternative computational methods such as elastic network models (ENMs) have become increasingly popular. These simple, coarse-grained models represent molecules as beads connected by harmonic springs; the system's motions are solved analytically by normal mode analysis. In the past few years, many different formalisms for performing ENM calculations have emerged, and several have been optimized using all-atom MD simulations. In contrast to other studies, we have compared the various formalisms in a systematic, quantitative way. In this study, we optimize many ENM functional forms using a uniform dataset containing only long (> 1 μs) all-atom MD simulations. Our results show that all models once optimized produce spring constants for immediate neighboring residues that are orders of magnitude stiffer than more distal contacts. In addition, the statistical significance of ENM performance varied with model resolution. We also show that fitting long trajectories does not improve ENM performance due to a problem inherent in all network models tested: they underestimate the relative importance of the most concerted motions. Finally, we characterize ENMs' resilience by tessellating the parameter space to show that broad ranges of parameters produce similar quality predictions. Taken together our data reveals that choice of spring function and parameters are not vital to performance of a network model and that simple parameters can by derived "by hand" when no data is available for fitting, thus illustrating the robustness of these models.

Computational reconstruction of multidomain proteins using atomic force microscopy data

Classical structural biology techniques face a great challenge to determine the structure at the atomic level of large and flexible macromolecules. We present a novel methodology that combines high-resolution AFM topographic images with atomic coordinates of proteins to assemble very large macromolecules or particles. Our method uses a two-step protocol: atomic coordinates of individual domains are docked beneath the molecular surface of the large macromolecule, and then each domain is assembled using a combinatorial search. The protocol was validated on three test cases: a simulated system of antibody structures; and two experimentally based test cases: Tobacco mosaic virus, a rod-shaped virus; and Aquaporin Z, a bacterial membrane protein. We have shown that AFM-intermediate resolution topography and partial surface data are useful constraints for building macromolecular assemblies. The protocol is applicable to multicomponent structures connected in the polypeptide chain or as disjoint molecules. The approach effectively increases the resolution of AFM beyond topographical information down to atomic-detail structures.